ART Artificial Reasoning Toolkit Evolving a complex system

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ART Artificial Reasoning ToolkitEvolving a
complex system
Spss training day 03-05-2004
Marco Lamieri lamieri_at_econ.unito.it
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• Agenda
• What is a genetic algorithm and how it works
• Some improvement to the method, the ART project
• Move to real world with an industry application
  the Penelope project
• References

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The idea

• Starting from Survival of the fittest Darwin,
  1959
• Genetic Algorithms (GA) are evolutionary programs
  that manipulate a population of individuals
  represented by fixed-format strings of
  information.
• The background theory is the artificial
  adaptation discussed by Holland Holland,1992.
• GA are used to solve real-world optimization
  problems within a very large solution space and
  non well defined problems.

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How does a GA work

• An initial population of individuals (solutions)
  is generated
• individuals represent potential solutions to the
  given problem and are described as binary
  strings
• each character in the individuals data string is
  called a gene and each possible value that the
  gene can take on is called an allele.
• Using a fitness proportional approach parents and
  individuals that are going to survive to the next
  generation are selected
• The selected individuals are evolved by means of
  reproduction using two operators
• crossover,
• mutation.
• Process go on untill the population converge to a
  specific individual.

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Example (square root of 2)

• The solution space is bounded between 0 and 1.
• We use a binary representation on 10 digits.
• There are 1024 numbers 210, starting from 0
  and ending at 1023 210 -1.

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Generate random population

• A population of solutions is generated randomly.
• For the square root problem, a fixed number of 10
  character binary strings are generated randomly.

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Define the fitness function

• Darwinian evolution of a population implies that
  the strongest individuals will probably survive.
• The fitness of an individual is a numerical
  assessment of that individuals ability to solve
  the problem - it is the ability of the individual
  to satisfy the requirements of the environment.
• In terms of the square root problem, the perfect
  individual is the numerical value approximated by
  1.414213562373.
• In economic problems,the profit can be used to
  generate a fitness function

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Selection process (roulette wheel)

• To select individuals is used the roulette wheel
  technique.
• The roulette wheel implementation implicitly
  forces fitness-proportionate reproduction.
• Selection is divided in 2 steps
• Individuals that are going to survive to the next
  generation are selected
• Individuals that are going to reproduce are
  selected.

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Crossover

• Crossover swaps some of the genetic material of
  two individuals, creating two new individuals
  (children), who are possibly better than their
  parents.

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Mutation

• In order to recover from this loss of genetic
  material, the individuals are allowed to change
  their genes randomly.

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Convergence

• John Hollands Schema Theorem Holland, 1992 is
  widely accepted as mathematical proof that the
  genetic algorithm, due to its fitness-proportionat
  e reproduction, converges to better solutions.
• Via the convergence method is possible to solve
  non well-defined problems where the best
  solution is not known a priori.

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Remarks

• There is no ultimate goal or problem that must be
  solved by natural evolution.
• Evolution itself does not guarantee the creation
  of fitter individuals.
• The GA use a fuzzy logic that not always lead to
  the best solution but to a good one.
• The algorithm is problem independent.

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ART Some improvement to the method

• ART, starting from John Holland's work,
  introduces some extensions and innovations
• extended alphabet each gene can be represented
  by up to 32000 values. In a standard
  representation the genes have a binary alphabet
  and can become meaningless. With the extended
  alphabet each allele can be a meaningful part of
  the solution and the translation process is
  easier.
• multi genome the multi genome schema give a
  high degree of freedom to the user in formalizing
  problems in which coexist different binded
  aspects.
• rescale fitness operatorthe natural selection
  process has been modified in order to improve
  efficiency and manage negative fitness values.
• univocal genome using this option each value of
  the alphabet is unique within the genome.

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An industry application the Penelope Project

• Penelope is an optimizing automated production
  planning engine.
• It is mainly applied to the textile industry.
• Penelope, consists of
• Enterprise Simulator (ES)a model of the firm's
  supply chain developed in Swarm.
• Genetic algorithm (GA) searching the solutions
  space to find the best production plan.

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The Enterprise Simulation

• Daily about 200 bulk orders arrive whit a defined
  delivery deadline
• Delay has economic value in term of customer
  satisfaction
• There are 20 machines available for the process
• Each machine can perform different operations
  with setup costs and setup time.
• A limited number of workers has to take care of
• machine set up
• patrolling
• ? Economic value of the production plan(fitness)

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The algorithm

• Solution space is
• Evaluating this number of solutions via brute
  force would take millions of years.
• The GA solve it in about 20 minutes.
• The individual is defined by
• 1 univocal genome with order number
• 1 random genome with machine number
• ? The priority is derived from the combination of
  the two genomes

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Results

• scheduling time reduction of nearly 80
• Random planning ? cost 100
• Fifo standard ? cost 60
• Human planner ? cost 40
• Penelope ? cost 25
• wider elaboration cases set (non obvious plan)
• best cost/time rate solution
• disposer software costs reduction (50)
• economic saving in terms of skilled resources
• more knowledge on production process and precise
  prediction of production time give strong
  contractual power to the enterprise
• overall increase of the performance of the
  company that can be more then 2 of the yearly
  value-added.

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References

• ART project http//eco83.econ.unito.it/golem
• Penelope project http//www.penelopeproject.org
• This presentation is available at
  http//eco83.econ.unito.it/golem/ppt/20040503-sp
  ss-art.ppt
• For any further information
• lamieri_at_econ.unito.it

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Questions ?